
Course unit
PLANAR ALGEBRIC CURVES
SCM0014408, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2015/16
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/03 
Geometry 
7.0 
Mode of delivery (when and how)
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Practice 
3.0 
24 
51.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
Examination board
Board 
From 
To 
Members of the board 
6 Curve Algebriche Piane  2017/2018 
01/10/2017 
30/09/2018 
BERTAPELLE
ALESSANDRA
(Presidente)
FIOROT
LUISA
(Membro Effettivo)
CAILOTTO
MAURIZIO
(Supplente)
CANDILERA
MAURIZIO
(Supplente)
KLOOSTERMAN
REMKE NANNE
(Supplente)
NOVELLI
CARLA
(Supplente)

Prerequisites:

Prerequisites: algebra and geometry courses of the first and second year. 
Target skills and knowledge:

The aim of the course is to introduce students to the study of fundamental (elementary) algebraic curves in the affine and projective plane:
singular points, tangents, intersection, local analysis; classification of cubics and group law on elliptic curves. 
Examination methods:

The final examination consists of two parts, a written one and an oral one. The written test can be splitted in two partial tests ("compitini"). 
Assessment criteria:

The written part is devoted to the study of the elementary aspects of a plane algebraic curve and to solving simple problems on theoretical topics of the course. The oral exam is intedended to evaluate theoretical skills acquired during the course and the ability to apply them. 
Course unit contents:

After recalling affine and projective spaces, we will study geometric properties of affine and projective curves by introducing algebraic tools that serve the purpose. These are the principal topics:
singular points and their tangent complexes, rational curves, polar curves; inflection points, Hessian curves (algebraic tool: algebraic differential calculus for polynomials).
Classification and geometry of the cubics; elliptic curves.
Intersection of plane curves, Bezout's theorem (algebraic tools: the resultant of two polynomials and the discriminant).
Local study of curves: branches, places, centers (algebraic tools: formal power series and Puiseux series). 
Planned learning activities and teaching methods:

Lectures on a chalkboard. Possible use of a tablet. 
Additional notes about suggested reading:

The course is based on the course notes "Curve Algebriche Piane" by Maurizio Cailotto.
Exercises of the past exams are collected in a ebook. Both sources will be available at the elearning page. 
Textbooks (and optional supplementary readings) 


